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A cubic polynomial is a polynomial of degree 3. A univariate cubic polynomial has the form f(x) = a3 x3 + a2 x2 + a1 x + a0. An equation involving a cubic polynomial is called a cubic equation. A closed-form solution known as the cubic formula exists for the solutions of an arbitrary cubic equation.
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Practice Test/Quiz or MCQ (Multiple Choice Questions) with Solutions o...
A cubic polynomial is a polynomial of degree 3. A univariate cubic polynomial has the form f(x) = a3 x^3 + a2 x^2 + a1 x + a0. An equation involving a cubic polynomial is called a cubic equation. A closed-form solution known as the cubic formula exists for the solutions of an arbitrary cubic equation.
Practice Test/Quiz or MCQ (Multiple Choice Questions) with Solutions o...
Understanding Polynomials
Polynomials are mathematical expressions that consist of variables and coefficients, combined using addition, subtraction, multiplication, and non-negative integer exponents. The degree of a polynomial is the highest exponent of the variable in the expression.
What is a Cubic Polynomial?
A cubic polynomial is specifically defined as a polynomial where the highest degree (or exponent) of the variable is 3. This means that in a cubic polynomial, you will find terms that are raised to the power of 3, along with possibly lower degree terms (like squared or linear terms).
Example of a Cubic Polynomial
An example of a cubic polynomial is:
- P(x) = 2x^3 + 3x^2 - 4x + 5
In the above polynomial:
- The term 2x^3 has the highest degree of 3.
- Other terms (3x^2, -4x, and 5) have lower degrees (2, 1, and 0, respectively).
Why is the Correct Answer Option 'B'?
- The question asks for the degree of a cubic polynomial.
- Since the highest exponent in a cubic polynomial is 3, the correct answer is option 'B'.
Summary
- A cubic polynomial has a degree of 3.
- It may include multiple terms, but the defining characteristic is the presence of the x^3 term.
Understanding the concept of polynomial degrees is crucial for recognizing different types of polynomials and their properties in mathematics.